The picture tube in an old black-and-white television uses magnetic deflection c

Question

The picture tube in an old black-and-white television uses magnetic deflection coils rather than electric deflection plates. Suppose an electron beam is accelerated through a 46.6-kV potential difference and then through a region of uniform magnetic field 1.00 cm wide. The screen is located 11.0 cm from the center of the coils and is 54.4 cm wide. When the field is turned off, the electron beam hits the center of the screen. Ignoring relativistic corrections, what field magnitude is necessary to deflect the beam to the side of the screen? mT

Explanation / Answer

angle of defelction tan theta = (27.2/11)

theta = 68 deg

then sin 68 = 1/R

radius R = 1/sin 68

R = 1.078 cm

apply centripetal force = magnetic force

i.e mv^2/r = qvB,

so speed v = sqrt(2eV/m)

where m = mass o the charged particle

v = velocity, r = radius ,

q = charge = 1.6*10^-19 C

v^2 = (2 * 1.6 e -19 * 46600)/(9.11 e-31)

v = 1.279 *10^8 m/s

B = magnetic field

so now , so as r = mv/qB

B = mv/qr = (9.11 e-31 * 1.279 e 8)/(1.6 e -19 * 0.01078)

B = 0.067 Tesla = or 67.5 mT

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